In synchronous data transmission systems, equalizers are provided for attenuating the intersymbol interference effects (see Lucky R. W., "Automatic equalization for digital communication", Bell Syst. Tech., J., 1965, 44, pp. 574-588), i.e. the undesirable effects of each symbol on the others due to the non-ideality of the frequency response of the transmission channel.
In particular, transversal filter equalizers operating in the time domain are known. They consist of a tapped delay line, i.e. a chain of delay elements. At the output of each delay element there is provided a variable gain multiplier (cell grain). The multiplier outputs are added to provide a sample on which the decision regarding the transmitted symbol is made. The decision element output constitutes the so-called decided signal, which, assuming no errors, should be equal to the signal fed into the channel.
The choice of the total cell gains defines the performance of the equalizer. If this gain total is fixed and constant, then the equalizer is a fixed equaliser, whereas if this total is variable by being adapted to the transmission channel characteristics, the equalizer is an adaptive equalizer. There are also "preliminary" equalisers, ie. able to be adapted to the channel characteristics, and, once adapted, to maintain the gain total fixed and constant.
The present invention relates to adaptive equalizers.
The criterion of gain total adaptation is to minimise the mean square value of the difference between the samples at the equalizer output (before the decision) and the corresponding decided signals (means square error). For a given channel, the mean square error is a function of the total gain of the multipliers. In practice, the mean square error is minimized in the following manner: the gain values are chosen (initially in an arbitrary manner, then gradually adjusting as suitable); with this configuration, non-zero differences between the output samples and the corresponding decided symbols are obviously found at the equalizer output. Using these differences together with the signals present at the equalizer input, the gains are modified so as to attain a minimum mean square error. It can be shown that this configuration exists, and is unique (see Gersho A., "Adaptive equalization of highly dispersive channels for data transmission", Bell Syst. Tech. J. 1969, 48 pp. 55-70).
The mean square error is minimised by estimating its gradient on the basis of the input sequence, the output sequence and the decided sequence, and the gains are modified in the opposite direction to the gradient.
If the surface which defines the mean square error (which can be likened to a paraboloid) is round, the gradient is always directed towards the point corresponding to the minimum means square error. However, if this curve is somewhat "squashed", this is not true.
A problem present in known adaptive equalizers is to rapidly attain the minimum mean square error configuration (optimum configuration), and auto-orthogonalizing equalizers have already been proposed for this purpose (see Gitlin R. D., Ho E. Y., Mazo J. E., "Passband equalization of differentially phase-modulated data signals", Bell Syst. Tech. J. 1973, 52, pp. 219-298). The principle of auto-orthogonalization consists of transforming coordinates so that the surface representative of the mean square error is transformed into a round surface, i.e. so that the auto-values of the matrix which defines it all become equal. This theoretically allows convergence to the optimum configuration in a single iteration (correction). In practice, the estimated gradient is premultiplied at each iteration by suitable matrices so that the direction of the thus modified vector always passes through the minimum which is being sought.
The adaptive auto-orthogonalizing equalisers of the type briefly described operate in the time domain, i.e. they operate directly on the time samples of the signals received.
There are also adaptive equalizers which operate in the discrete frequency domain, ie which operate on the discrete Fourier transforms of sample blocks (see Corsini P., Picchi G., Prati G. "Adaptive equalization of discrete channels via fast convolution techniques", IEE Proc., Part E, 128, pp. 239-244 Nov. 1981). Compared with equalizers operating in the time domain, adaptive equalizers of this type have considerable advantages both because of the simplification which they enable in the filtering operations, and because of the possibility of using the sample transforms for other subsequent processing operations (decoding, synchronisation etc.).